Since the appearing of the reduced gradient method given by Wolfe, many authors have tried to obtain the convergence of this method or of a modified form if it (see e.g. Luenberger). This method is designed to solve a non-linear problem subject to linear equality and bound constraints, use the principle of the variables decomposition into basic and non-basic variables and the computation of the pivot as an extension of the simplex method. It has been generalized to non-linear equality constraints by application of the implicit function theorem, this generalization is called the generalized reduced gradient method: GRG due to Abadie and Carpentier. This paper studies the adaptation of the GRG to the non-differentiable case by using bundle techniques introduced by Lemaréchal and applied to linear constraints by Bihain, Nguyen and Strodiot.
